Viscous versus inviscid instability of two-phase mixing layers with continuous velocity profile

We consider the temporal instability of parallel two-phase mixing layers. The viscous case is examined using a composite error-function velocity profile. The inviscid case is considered for the broken-line velocity profile, where the thickness of the boundary layer in each fluid next to the interface is chosen to match the viscous error-function profile at the interface and far away from it. Viscosity modifies the inviscid stability properties quantitatively, but we can also discern an additional unstable mode exclusively related to viscous shear. In the absence of interfacial tension, this mode dominates at large wavenumbers when the Reynolds number is sufficiently high. The various viscous modes cannot generally be attributed to either one of the phases due to mode mixing or exchange. For parameters resembling those of atomization experiments and applications, the most unstable wavelength and growthrate in the viscous case can exceed the inviscid values significantly. The viscous stability analysis also provides better agreement with recent experimental results for air and water than inviscid stability calculations.